Purpose and scope

This is an R Markdown document illustrating my stability analysis of the SARS-Cov2 S1 IgG antibody ELISA data. This data was generated by Ana, where 45 samples (1 full plate and a partial plate of 5 samples) were processed and read in 5 technical replicates each, each of which had 405nm absorbance readings taken at 15, 30, and 45 minutes.

The purpose of this document is to explore, visualize, and summarize the intra and inter-assay variability of these readings.

Visualizing the reaction development

To begin with, I visualize how the absorbance values develop over time for each plate (P_1032 and P_12345), for each replicate of the plate (A, B, C, D, and E). Each individual unknown sample is run in duplicate on each plate. The wells on the first half of the plate are drawn with solid lines, the wells on the second half of the plate are drawn with dotted lines.

There are a few important things to notice here:

Visualizing intra-assay variation

To get an idea of the intra-assay variation, I calculate three metrics from the absorbances (abs) of each unknown and negative control sample, \(i\), and replicates 1 and 2:

For the positive controls and blanks, the same metrics are calculated, but using all the wells of the same type for that plate, at that time point.

These three metrics are plotted as line plots below. There are a few important observations:

Absorbance range

Percentage difference

%CV

Next, I plot them as heatmaps where the labels underneath show the combination of plate ID and plate replicate (A to E). The x and y labels correspond to the plate coordinates. Note that the value for the blanks is shown in A6, the value for the negative control is shown in F6 and the value for the positive controls in G6. These plots just help us spatially refer the values to the position on the plates.

There are a few important observations:

  • for any particular plate, as you look from 15 minutes (top row) to 45 minutes (bottom row), there is a pattern where the intra-assay variation for a particular well propogates through time, i.e. if a sample has a large discrepancy between its two replicates at 15 minutes, that discrepancy will likely be there at 45 minutes
  • samples that start with a large discrepancy between their replicates tend to have smaller ranges and CVs at later time points
  • blanks tend to have small ranges but large percentage differences and CVs
  • in some plate replicates, the negative and positive controls have unexplained high CVs/ranges

Absorbance range

Percentage difference

%CV

Next, I plot each well as a point. These plots help us to compare the variation between the sample types and between each plate replicate. There are some important observations:

  • the positive controls are typically the most reproducible within each plate, followed by the negative control
  • there is quite a strong relationship between the control variation and the unknown variation: if the CV of the controls are high, the CV of the unknowns are also high
  • there is a large range of variation of the unknowns

Absorbance range

Percentage difference

% CV

Calculating intra-assay variation for each sample type

To summarize the intra-assay variation, I calculate the mean range, percentage difference, and % CV for each sample type, at each time point. The means ± 1 standard deviation are shown.

Note that for the positive control and the unknown samples, all three metrics decrease from 15 minutes to 30 minutes to 45 minutes. This data does not contain the information needed however, to conclude if this increase in precision comes at the cost of reduced assay sensitivity (the ability to discriminate positive cases).

Type Time Range Percent_diff CV
Blank 15 0.04 ± 0.02 48.43 ± 17.99 17.11 ± 6.32
Blank 30 0.09 ± 0.07 74.27 ± 31.6 29.76 ± 15.89
Blank 45 0.15 ± 0.13 89.75 ± 38.75 38.79 ± 22.07
Negative 15 0.01 ± 0.01 13.48 ± 9.19 9.53 ± 6.5
Negative 30 0.02 ± 0.02 12.55 ± 13.2 8.87 ± 9.34
Negative 45 0.03 ± 0.04 13.15 ± 15.02 9.3 ± 10.62
Positive 15 0.26 ± 0.17 11.69 ± 8.04 5.23 ± 3.76
Positive 30 0.21 ± 0.15 6.61 ± 4.91 2.85 ± 2.08
Positive 45 0.1 ± 0.05 3.04 ± 1.62 1.34 ± 0.7
Unknown 15 0.17 ± 0.14 11.99 ± 10.21 8.48 ± 7.22
Unknown 30 0.16 ± 0.16 8.36 ± 9.26 5.91 ± 6.55
Unknown 45 0.14 ± 0.16 6.24 ± 8.22 4.41 ± 5.81

Visualizing inter-assay variation

In addition to evaluating the variation in absorbances within the same plate, it's important to evaluate the variation in absorbances of the same sample across different plates. Here I repeat a similar methodology as for the intra-assay analysis.

To get an idea of the inter-assay variation, I calculate three metrics from the absorbances (abs) of each unknown and negative control sample, \(i\), in the same well across each plate replicate, \(j\). Here, \(n\) is the number of plate replicates.

This time, I'll start with the heatmaps. The interpretation is the same as before, except now we are looking at the variability of the absorbances of each well across multiple plate replicates.

There are a few important observations: - plate range and percentage difference increase with time, but % CV slightly decreases - discrepancies between plates at 15 minutes generally propogate through to 30 and 45 minutes - the range and percentage difference of absorbances between plates are high for the positive controls, while the CV is low. The opposite is true for the blanks and negative controls - there are no common spatial patterns as to which wells have the largest discrepancies between runs

Absorbance range

Percentage difference

% CV

Next, I plot these as points. This helps compare the sample type stability across plates. There are a few important observations: - the positive controls and many of the unknowns have a very large between-plate range of absorbance values. The opposite is true for the blanks and negative controls - Any change in stability with time is subtle or non-real - On plate P_1032, there are two clusters of unknown samples with different between-plate ranges, though this is not apparent for the other two metrics - the between-plate percentage difference and CV are relatively constant across sample types

Absorbance range

Percentage difference

% CV

Calculating inter-assay variation for each sample type

To summarize the inter-assay variation, I calculate the mean range, percentage difference, and % CV for each sample type, at each time point. The means ± 1 standard deviation are shown.

Note that, just like with the intra-assay variability, for the positive control and the unknown samples, all three metrics decrease from 15 minutes to 30 minutes. This data does not contain the information needed however, to conclude if this increase in precision comes at the cost of reduced assay sensitivity (the ability to discriminate positive cases).

Type Time Range Percent_diff CV
Blank 15 0.08 ± 0.03 100 ± 29.06 25.03 ± 7.35
Blank 30 0.11 ± 0.06 100 ± 42.56 39.65 ± 15.77
Blank 45 0.14 ± 0.1 100 ± 51.88 51.3 ± 20.24
Negative 15 0.11 ± 0.02 100 ± 17 11.71 ± 5.51
Negative 30 0.15 ± 0.04 100 ± 21.03 14.9 ± 7.39
Negative 45 0.2 ± 0.05 100 ± 23.14 17 ± 7.69
Positive 15 2.31 ± 0.44 100 ± 18.94 14.83 ± 1.17
Positive 30 3.14 ± 0.27 100 ± 8.53 6.69 ± 1.09
Positive 45 3.36 ± 0.11 100 ± 3.29 2.57 ± 0.59
Unknown 15 1.62 ± 0.74 100 ± 31.31 26.01 ± 7.7
Unknown 30 2.43 ± 0.83 100 ± 24.02 19.19 ± 8.83
Unknown 45 2.82 ± 0.73 100 ± 18.65 13.46 ± 9.27

Conclusions

Here are a summary of my thoughts based on this analysis: